Suppose that the price p (in dollars) and the weekly sales x (in thousands of units) of a certain commodity satisfy the demand equation 6p cubedplusx squaredequals850. Determine the rate at which sales are changing at a time when xequals10, pequals5, and the price is falling at the rate of $.40 per week.

9514 1404 393

  increasing 9000 units per week

Step-by-step explanation:

The price and sales relation is given as ...

  6p³ +x² = 850

Differentiating with respect to time gives ...

  18p²·p' +2x·x' = 0

Filling in the given values, we have ...

  18(5)²(-0.40) +2(10)x' = 0

  20x' = 180 . . . . . . add 180

  x' = 9 . . . . . . . . . . divide by 20

Sales are increasing at the rate of 9,000 units per week.

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt

45

step-by-step explanation:

to find a percentage, add a decimal in front and multiply it by the other number.

.25 times 180= 45